• 대한수학회논문집
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• 제11권4호
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• pp.983-996
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• 1996

In this paper, we show that $\Vert \xi \Vert_r = \Vert \sum_{i \in I}x_i x^*_i \Vert^{\frac{1}{2}}, \Vert \xi \Vert_c = \Vert \sum_{i \in I}x^*_ix_i \Vert^{\frac{1}{2}}$ for $\xi = \sum_{i \in I}x_i e_i$ in $M_n(H)$, that subspaces as Hilbert spaces are subspaces as column and row Hilbert spaces, and that the standard dual of column (resp., row) Hilbert spaces is the row (resp., column) Hilbert spaces differently from [1,6]. We define operator Hilbert spaces differently from [10], show that our definition of operator Hilbert spaces is the same as that in [10], show that subspaces as Hilbert spaces are subspaces as operator Hilbert spaces, and for a Hilbert space H we give a matrix norm which is not an operator space norm on H.

• 충청수학회지
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• 제31권3호
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• pp.343-352
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• 2018

We study the complete convergence for sequences of dependent random variables in Hilbert spaces. Results are obtained for negatively associated random variables and ${\phi}$-mixing random variables in Hilbert spaces.

• 대한수학회논문집
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• 제12권4호
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• pp.905-909
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• 1997

A characterization of Hilbert spaces is given in terms of four boundary points and two interior points of the unit sphere.

• 대한수학회지
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• 제40권2호
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• pp.207-224
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• 2003

Some weighted Ostrowski type integral inequalities for vector-valued functions in Hilbert spaces are given. Applications for quadrature rules with values in Hilbert spaces are also pointed out.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.813-837
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• 2022

In this paper we consider inverse problem for a general class of nonlinear stochastic differential equations on Hilbert spaces whose generating operators (drift, diffusion and jump kernels) are unknown. We introduce a class of function spaces and put a suitable topology on such spaces and prove existence of optimal generating operators from these spaces. We present also necessary conditions of optimality including an algorithm and its convergence whereby one can construct the optimal generators (drift, diffusion and jump kernel).

• 대한수학회보
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• 제33권1호
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• pp.35-38
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• 1996

The aim of this paper is to present a characterization of Hilbert spaces in terms of the lengths of four sides and two diagonals of a parallelogram.

• 대한수학회보
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• 제35권2호
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• pp.311-317
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• 1998

For Hilbert spaces H, K, a compact operator T: H $\rightarrow$ K, and column, row, operator Hilbert spaces $H_c,\;K_c,\;H_r,\;K_r,\;H_o, K_o$,we show that ${\parallel}T_{co}{\parallel}_{cb}={\parallel}T_{ro}{\parallel}_{cb}={\parallel}T_{oc}{\parallel}_{cb}={\parallel}T_{or}{\parallel}_{cb}={\parallel}T{\parallel}_4$.

• 대한수학회보
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• 제59권4호
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• pp.905-915
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• 2022

This paper studies the boundedness of integral operators on the Cesàro function spaces. As applications of the main result, we obtain the Hilbert inequalities, the boundedness of the Erdélyi-Kober fractional integrals and the Mellin fractional integrals on the Cesàro function spaces.

• 대한수학회논문집
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• 제32권2호
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• pp.333-352
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• 2017

In this research work, by using the random resolvent operator techniques associated with random ($A_t$, ${\eta}_t$, $m_t$)-monotone operators, is to established an existence and convergence theorems for a class of fuzzy system of random nonlinear equations with fuzzy mappings in Hilbert spaces. Our results improve and generalized the corresponding results of the recent works.

• 대한수학회논문집
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• 제35권2호
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• pp.547-563
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• 2020

We define a left quotient as well as a right quotient of two bounded operators between Hilbert spaces, and we parametrize these two concepts using the Moore-Penrose inverse. In particular, we show that the adjoint of a left quotient is a right quotient and conversely. An explicit formulae for computing left (resp. right) quotient which correspond to adjoint, sum, and product of given left (resp. right) quotient of two bounded operators are also shown.